# Frequentist notion of probability

The or rather one of the Frequentist interpretations of probability claims that the statement "The next coin toss )that is executed under conditions X) has a probability of 90% to land heads" simply means: "The next coin toss belongs to an infinite sequence of coin tosses that are executed under conditions X, and which have the limiting relative frequency 90%." Let (x1,x2, .... ) be the infinite sequence of coin tosses under condition X.

My question now is why this should give me any confidence that the next coin that I am interested in (and that is executed under conditions X) will land heads. It seems to me that the 90% are only relevant to my single case, if I make the additional assumption that the next coin toss that I am considering is somehow randomly chosen from this infinite sequence. Or alternatively I have symmetric evidence that the next coin toss be x1 or x2 or x3 or ... .

However I have never read anything similar to that from a defendant of the frequentist notion of probability

My real question is therefore whether:

1. All that (Probability-)Frequentists mean when they claim: "The next coin toss (that is executed under conditions X) has a probability of 90% to land heads" is really: "The next coin toss belongs to an infinite sequence of coin tosses that are executed under conditions X, and which have the limiting relative frequency 90%." or
2. Whether they actually mean something different and I just missunderstand them